


Three Chords and the Truth

by primeideal



Category: Anthropomorphism, Numbers (Anthropomorphic)
Genre: Bands, Gen, Mathematics, Quaternions, Song Lyrics, Yuletide 2017, Yuletide Treat
Language: English
Status: Completed
Published: 2017-12-25
Updated: 2017-12-25
Packaged: 2019-02-14 15:09:12
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 2,941
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/13010397
Author URL: https://archiveofourown.org/users/primeideal/pseuds/primeideal
Summary: The quaternions start a band!





	Three Chords and the Truth

**Author's Note:**

  * For [ariesspicy](https://archiveofourown.org/users/ariesspicy/gifts).



> While not the nominator, I was delighted to see this "fandom" in the tagset!
> 
> Thanks to dblanc for betaing.
> 
> I once participated in a math program during which it occurred to some of us that the "Pure Imaginary Quaternions" sounded like a great name for a band. That's basically it.

_-i_ was feeling negative.

"Just because you got named first doesn't mean you have the right to go acting all better than me!" she sulked. "I'm no lesser than you, I can't be ordered! Like those realists can tell us apart anyway."

 _i_ was taken aback. "Well, what am I supposed to do about it?"

"I don't know," _-i_ pouted.

"It’s _i doesn't_ know," _i_ felt inclined to interrupt.

"Only when you're involved."

"Well, I'm sorry you feel that way, but it's really not my problem."

"We could conjugate," _-i_ said flirtatiously.

 _i_ was taken aback. "I'm really not in the mood."

"Well, you should reflect on it some more," _-i_ demanded.

Eager to escape _-i_ 's cynicism, _i_ drifted across the complex plane, and finding little to amuse her there, climbed into quaternion space. _j_ and _k_ were locked in their ancient dance, captivated by each other's images, their moods swinging from anger to joy at the slightest provocation.

Fortunately, _k_ seemed to be in a good mood when he noticed _i_ pass by. "What's up?" he called.

"Not much," she sighed. " _-i_ is whining again."

"Tell me about it," said _j_. "I just had to write an angry letter to _-j_ , he keeps thinking it's funny to spin me around when I'm not looking."

"Can you complain?" _i_ asked. "It's not like you treat him much better."

"You really need new hobbies," said _k_.

"I'm done taking advice from you," _j_ retorted. "It's all 'going for riverside walks this' and 'stonework that,' you're boring as all get-out."

"And yet everyone still wants to scale with me. Remember that time 4 wanted to make an _example_ with me? Man, 3+4 _k_ was famous on norm-calculating day!"

"Ugh, not the four-dimensionals," _i_ shuddered. "No offense, but I came here to talk to you guys. You know, the pure imaginary quaternions."

"Elitist," _j_ teased.

"What?" said _i_. "It'd be a totally cool, uh, band name."

"You mean us?" _k_ asked. "Form a band?"

"Come on," said _j_. "It'd be a lot more fun than most of the stuff we do around here. Squaring, multiplying, making vectors? I'm ready for a change of pace."

"Do you even know how to sing?"

"I do," said _i_. "If you know how to play instruments, or something..."

"We can figure it out," _j_ said. "How hard can it be?"

 _k_ and _i_ exchanged glances. "It's worth a try," _k_ finally agreed. "Anything to break up the monotonicity around here, yeah?"

* * *

_i_ waited outside the bus stop for pi to show. It turned out that writing lyrics and simple melodies wasn't so hard, but in order to start transcribing accompaniment for the others, she needed something more. So she'd read the classifieds in the _Daily Digit_ , looking for someone to get in contact with. Pi had had just what she needed.

"Are you sure you want to sell this?" _i_ asked, turning the guitar over in her hands. "It's beautiful."

"Sure," pi shrugged. "e and I are back on again."

 _i_ squinted. "So what, your entire social life is revolving around him? That doesn't sound very healthy."

"No, not like that," pi laughed. "I just mean, I'm not in the mood to write angsty breakup songs anymore."

 _i_ snorted. "If the band goes well, I'm not trading this back to you next time you dump him."

Pi shrugged. "What can I say? Being in love makes everyone irrational."

"Speak for yourself," _i_ said, then paused. "But seriously, don't let him overpower you."

"I'm fine," said pi. "Really."

"All right. Well, not to jinx anything, but if it doesn't work out, you know you're always welcome to crash at my place? One good turn deserves another, and all." _i_ handed over her payment.

"Of course," said pi. "Good luck with your band."

"Thanks!" _i_ grinned.

Pi headed off on the next bus, and _i_ slowly began the long walk home. It was great having her fellow quaternions to compose with, but every once in a while, she got jealous of numbers who could commute.

* * *

_j_ plucked at the strings of his bass guitar. Then he plucked at them again. And again.

"I just think we should invest in some electric instruments," he said, "the reverb would be much cooler."

"We haven't even gotten off the ground yet," _k_ warned, "don't get ahead of yourself."

"Speak for yourself, you get to do those drum stings when someone makes a terrible pun," said _j_. "What more can you want?"

"Can we focus?" _i_ asked. "I want to run the new song again."

"Sure," said _k_.

"All right," _i_ said. "A one, and a two, and a one, two, three, four..."

"How long does that go on?" _k_ asked.

"Does what go on?"

"The introduction. Do you just count up to even numbers? Powers of two? How many are we going to sit through? Because iterating that sequence could go on for quite a while."

"Uh, I was just going to start the song."

"Why do you even have an introduction then?"

"I guess it's tradition."

 _k_ shrugged skeptically. "Fine."

"All right," said _i_ , a little shaken. "Uh...ready, set, go?"

_Like a sequence spiralling inward_  
_But that won't converge_  
_Like an unsolved polynomial_  
_I can't shake the urge_  
_To split it into pieces_  
_I'm so paranoid_  
_That no matter where I turn_  
_I cannot fill this void_

_I'm incomplete_  
_Just a bounded space_  
_I'm incomplete_  
_How can I know my place_  
_When there's nowhere to stand_  
_On my own two feet_  
_There's no way to go on_  
_When I'm incomplete._

"I haven't written the next verse yet," _i_ explained. "But I figure another chorus and then maybe you could have a solo, _j_."

"Isn't this a little...dark?" _j_ asked.

"Well, we're a rock band, aren't we? We're supposed to have plenty of screaming and yelling."

"I don't know, I just thought you could croon a little more. Ask for something to complete you."

 _i_ wrinkled her nose. "What, you think this is some kind of romance metaphor? We're dealing with topology here! Or algebra, I haven't really decided."

"Just saying. I don't want you to wear out your vocal chords or anything."

"Thoughtful. All right, _k_ , I think you can go a little more wild with the rhythms on the chorus in particular, but maybe wait and see what we decide to do for the last time through..."

* * *

Their first gig was at a rundown place called "Zeta's." The proprietor, .5, did not seem to be in a mood to deal with them, and _k_ seemed skeptical as to what genre the bar actually specialized in. "I'll be able to get some of my friends to show up," _i_ said with bravado, "that's all that matters."

"You don't have friends," _k_ pointed out, "that's why you started a band."

"I have you!"

"Yeah, and how long do friendships last when musical egos get in the way?"

"Don't talk like that," said _j_ , fussing with his bass strings yet again. "Tonight's our big break. Our _first_ big break."

The light on the stage produced an extreme glare, and it was impossible for them to see anything in the audience; were the other numbers attentive? Pleased? Sober? There was no way of knowing. All they could do was trust each other and the music that flowed between them.

"Okay," _i_ said. "Ready, set, go."

_Sometimes I wake up twice as tall_  
_Or maybe half as wide._  
_Sometimes I wake up upside-down_  
_Or jumbled-up inside._  
_I see myself within the mirror_  
_The mirror is true and then,_  
_Put myself back together to_  
_Do it over again._

_Wake up transformed--_  
_I slip and slide and spin_  
_Wake up transformed--_  
_The world is whirled within_  
_If there's a norm_  
_Upon this space then I don't care_  
_Because I'll come back home_  
_Someday and not be sure that I'm all there._

She surged through the chords and launched into another verse, the others' enthusiasm propelling her forward.

A wave of applause followed their opener, becoming increasingly tepid as they played through their setlist. By the time they finished, .5 seemed ready to hustle them out. _i_ caught a glimpse of her multiple 14 _i_ looking cheery, if disengaged, as they headed out through the back door. The instruments felt much heavier than they had upon their entry.

"That was awesome," she emphasized.

"Yeah," _j_ said, "and we probably got some exposure."

"Exposure? Here?" _k_ snorted. "Unless you were 'exposing yourself,' and I really don't want to think about that mental image, I have no idea who'd be listening to us in a dump like this."

"Lots of numbers," said _i_.

"Finitely many. And none who have an influential neighborhood of associates."

"Let's take it slow," _j_ yawned, pausing to set down his bass. "In some cases literally."

* * *

But it wasn't long before _j_ 's dreams began expanding rapidly again. "We should go on tour."

"Where?" _k_ asked. "Everyone should be able to come around to us if they wanted."

"So I've started looking up some places," said _j_. "Uh, there's Zenzizenzic's. 256 usually hosts there, she's not super hip but has good taste, I think she'd be open to us."

 _i_ began scribbling notes. "That's a little far off down the real axis, but good to know. Where else?"

"Well, out in the opposite direction there's the Rollover. A little sketchy clientele, but they go for that binary ambiance."

"Ugh, not the two's complement people," _k_ shuddered. "At that rate we might as well just visit the _p_ -adics and you know how _they_ are."

"We're just brainstorming," said _i_.

"And then there's the Point at Infinity, up on the Riemann Sphere. I don't know about us instrumentalists, but _i_ , they’d probably love your vocals! And then maybe once we're there we can swing by the Inaccessible Cardinal--it's a really selective stage, you definitely have to be someone to play it--and finish off at the Hilbert Ballroom?"

"Whoa, whoa, slow down." _i_ jotted down all of _j_ 's suggestions. "Have you thought about how we're going to handle all of this, transportation wise?"

"Uh," said _j_ , "I mean as far as carrying our instruments goes? I guess we could get a roadie or someone to help us."

"I mean in terms of getting from place to place. That's a lot of travel. Have you thought about what metric you're going to put on all those spaces?"

"I guess the trivial one is right out?"

"Quite. If we're actually going to put on five different shows in a row, we need to plan the optimal route to save on travel time."

"Makes sense," said _k_. "So, what? Write down all the possible orders we could do it in, calculate the travel time for each one, then figure out which is minimal?"

"Five factorial is...a hundred and twenty," said _i_. "No way I'm doing that."

"Okay," said _j_. "Maybe a tour was a little overambitious."

* * *

Despite .5's dour mood, they'd landed another gig at Zeta's. After a list of up-tempo songs, _i_ segued into a quieter ballad for the finale.

_Just like a function_  
_I want to compose_  
_Put letters in order_  
_You know how it goes_  
_Until in their sequence_  
_They rise above prose_  
_And I've forged a chain that will last._

_Just like a function_  
_Bounded by a border_  
_I want to arrange_  
_From chaos to order_  
_Until it re-echoes_  
_From every recorder_  
_And sounds something new, something vast._

"Come back to my place," _j_ invited them afterwards, "I have fans."

"Fans?" _k_ snorted. "You mean friends from out of town you made come?"

"Sure. You should still come."

"Whatever," said _k_.

"All right," said _i_. "Maybe they'll want us to do a gig."

 _j_ 's friends did not look much like agents. They did, however, include a mysterious woman called _l_. "Excellent show," she smiled. "A little derivative in parts, no doubt, but very creative."

"How come we've never met you?" _k_ asked.

" _l_ doesn't like to associate with us riffraff," _j_ said.

"Now, now," said _l_ , reaching for a bottle. "I live a very busy life, but that doesn't mean I can't have fun every now and then. Would you rock stars like to expand your mind with me?"

"I need to stay sharp," _i_ said. "We still have lots of writing to do."

"Live a little!" _j_ protested, having a swig.

 _i_ took a drink, and started to feel dizzy. She saw lattices blurring and flashing in front of her eyes, and the noise of the party faded.

* * *

_i_ woke up with a headache and glanced over at her phone. A message from _k_ explaining that he'd walked her home after the party, and a missed call from a symbol she didn't recognize. Curious. She thanked _k_ , then returned the call.

"Hello?" asked the unfamiliar voice.

"This is _i_ ," she answered, then hopefully added "from the Pure Imaginary Quaternions."

"Aha! Great to hear from you. My name is Aleph-Null, and I have an exciting proposition for you..."

Later that day, she relayed the message to the others. "He wants to be our agent."

"That's amazing!" said _j_. "We should go for it."

"But there's a catch," _i_ hastened to add. "We'd have to perform with like his choice of opening act. I've looked her up, and she seems kind of a diva."

"So what?" said _k_. "Some contrast between us and a soloist would be fine."

"I'm not sure," said _i_. "We could potentially be losing some of our freedom."

"What freedom?" _j_ asked. "To play at Zeta's when we're lucky enough? We're stuck here as it is. It's not like he's said anything about what kind of music he wants us to write, is it?"

"Well, no."

"And he'd pay us to write a whole album?" _k_ asked.

"I mean, if we get that far."

"All right. I say we should go for it."

"Agreed," said _j_. "Sorry, _i_ , I think you're outvoted."

 _i_ scowled. "There's gotta be a fairer voting system."

 _k_ snorted. "Says you."

* * *

"Mike check!" warbled phi. "Mike check, here we gooo..."

On stage at the _Mobius Bandshell_ , the soloist tapped the microphone and pronounced it to her satisfaction while _i_ and _k_ exchanged skeptical glances. Before they could mutter under their breaths, Aleph-Null approached.

"Splendid!" he thundered. "Pleasure to see you all."

"Right," said _j_. "I'll just be...plugging my bass in."

"You don't--" _i_ began. _k_ elbowed her. "Right," she said, "it's good to be here. Thank you so much for your encouragement."

"My pleasure," said Aleph-Null. "The record coming along?"

"Slowly," said _k_. "We have a lot of different ideas bouncing around."

"Well, this will be a fine spot to practice some of them out," he smiled. "Let me know if you need anything!"

"Okay," said _j_ , re-emerging, "maybe you were right."

"Too late now," said _i_ , leading them backstage, "we'd better make the most of it. Let's go tune up."

From behind the stage, they could hear as the audience filtered in, and phi began her short set.

_The flowers and the pinecones_  
_The starfish in the sea_  
_They all can feel the magic_  
_That's flowing over me_  
_So reach out, touch somebody_  
_You care for very much_  
_And sooner than you know it_  
_You'll feel the golden touch_

_Look around you and behold_  
_Everything is turning gold_  
_Harmony with all the earth_  
_Feel the magic brought to birth._

"Gag me," _k_ shuddered.

"Not now," said _j_ , "we're going on stage."

"Not soon enough."

"Maybe we could evacuate?" said _i_ , staring at another back door.

"Sounds like a plan," _k_ muttered.

"I was kidding," _i_ rushed to add, but she squinted at it before she turned back to tuning her guitar.

Despite their groaning, phi's opening act was soon through, and it was time for them to take the stage. The Mobius Bandshell was better lit than Zeta's, and the audience seemed to be clamoring to see them! Fired up, the Quaternions launched into their newest single.

_I've got a torus_  
_And it's tasty to eat_  
_I've got a torus_  
_What a wonderful treat_  
_If I zoom in_  
_Then it's locally flat_  
_If I zoom out_  
_There's a big hole and that's_  
_Where stuff ebbs and flows_  
_And it's wonderfully porous_  
_We go together,_  
_Just me and my torus._

_I wrapped some paper_  
_Till the edges would merge_  
_I made a torus_  
_Got a real hungry urge._  
_Now nothing more_  
_Can ever come between us_  
_My manifold_  
_Of a singleton genus._  
_I wrapped some paper,_  
_Bound the edges with paste_  
_I made a torus,_  
_Of spectacular taste!_

The crowd roared its approval, except for a few who questioned whether it had anything to do with the building they were in, and were firmly told otherwise by Aleph-Null. The quaternions rocked on.

When it was all over, giddy and flush with excitement, Aleph-Null came to shake hands with them backstage. "Thank you," said _i_. "I have to say, I really do appreciate it."

"Of course!" he grinned. "I see great things in your future."

"May I ask you a question?"

"Certainly."

"What does this mean?" She indicated the door; _In case of emergency, cut along this line._

"Ah, yes. It's to expand the building in case of an orientability crisis."

"Hmm. Okay, thanks."

"Though I recommend you simply exit by it tonight. You see, you have some very vocal fans outside the main stage, and I wouldn't want you to get overwhelmed."

"Sounds good," said _j_. "Thank you."

"We have fans?" _i_ gasped. "Who are they?"

Aleph-Null smiled. "The Lie Groupies."


End file.
